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Subtractive synthesis techniques often require a wideband excitation source such as a pulse train to drive a time-varying digital filter. Traditional rectangular pulses have theoretically infinite bandwidth, and therefore always introduce aliasing noise into the input signal. A band-limited pulse (BLP) source is free of aliasing problems, and is more suitable for subtractive synthesis algorithms. The mathematics of the band-limited pulse is presented, and a LabVIEW VI is developed to implement the BLP source. An audio demonstration is included.
This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you:
•Apply LabVIEW to Audio Signal Processing
•Get started with LabVIEW
•Obtain a fully-functional evaluation edition of LabVIEW


Subtractive synthesis techniques apply a filter (usually time-varying) to a wideband excitation source such as noise or a pulse train. The filtershapes the wideband spectrum into the desired spectrum. The excitation/filter technique describes the sound-producing mechanism of many types of physical instruments as well as the human voice, makingsubtractive synthesis an attractive method for physical modeling of real instruments.

A pulse train , a repetitive series of pulses, provides an excitation source that has a perceptible pitch, so in a sense the excitation spectrum is "pre-shaped" before applying it to a filter.Many types of musical instruments use some sort of pulse train as an excitation, notably wind instruments such as brass (e.g., trumpet, trombone, and tuba) and woodwinds (e.g., clarinet, saxophone, oboe, and bassoon). Likewise, the humanvoice begins as a series of pulses produced by vocal cord vibrations, which can be considered the "excitation signal" to the vocal and nasal tract that acts as a resonant cavity to amplify and filterthe "signal."

Traditional rectangular pulse shapes have significant spectral energy contained in harmonics that extend beyond the folding frequency (half of the sampling frequency). These harmonics are subject to aliasing , and are "folded back" into the principal alias , i.e., the spectrum between 0 and f s / 2 . The aliased harmonics are distinctly audible as high-frequency tones that, since undesired, qualify as noise.

The band-limited pulse , however, is free of aliasing problems because its maximum harmonic can be chosen to be below the folding frequency. In this module the mathematics of the band-limited pulse aredeveloped, and a band-limited pulse generator is implemented in LabVIEW.

Mathematical development of the band-limited pulse

By definition, a band-limited pulse has zero spectral energy beyond some determined frequency. You can use a truncated Fourier series to create a series of harmonics, or sinusoids, as in :

x ( t ) = k = 1 N sin ( 2 π k f 0 t ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG0bGaaiykaiabg2da9maaqahabaGaci4CaiaacMgacaGGUbGaaiikaiaaikdacqaHapaCcaWGRbGaamOzamaaBaaaleaacaaIWaaabeaakiaadshacaGGPaaaleaacaWGRbGaeyypa0JaaGymaaqaaiaad6eaa0GaeyyeIuoaaaa@49C4@

The screencast video shows how to implement in LabVIEW by introducing the "Tones and Noise" built-in subVI that is part of the "Signal Processing" palette. The video includes a demonstration that relatesthe time-domain pulse shape, spectral behavior, and audible sound of the band-limited pulse.

Download the finished VI from the video: blp_demo.vi . This VI requires installation of the TripleDisplay front-panel indicator.

[video] Band-limited pulse generator in LabVIEW using "Tones and Noise" built-in subVI

The truncated Fourier series approach works fine for off-line or batch-mode signal processing. However, in a real-time application the computational cost of generating individual sinusoids becomes prohibitive, especially when a fairly dense spectrumis required (for example, 50 sinusoids).

A closed-form version of the truncated Fourier series equation is presented in (refer to Moore in "References" section below):

x ( t ) = k = 1 N sin ( k θ ) = sin [ ( N + 1 ) θ 2 ] sin ( N θ 2 ) sin ( θ 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG0bGaaiykaiabg2da9maaqahabaGaci4CaiaacMgacaGGUbGaaiikaiaadUgacqaH4oqCcaGGPaGaeyypa0Jaci4CaiaacMgacaGGUbWaamWaaeaacaGGOaGaamOtaiabgUcaRiaaigdacaGGPaWaaSaaaeaacqaH4oqCaeaacaaIYaaaaaGaay5waiaaw2faaaWcbaGaam4Aaiabg2da9iaaigdaaeaacaWGobaaniabggHiLdGcdaWcaaqaaiGacohacaGGPbGaaiOBamaabmaabaGaamOtamaalaaabaGaeqiUdehabaGaaGOmaaaaaiaawIcacaGLPaaaaeaaciGGZbGaaiyAaiaac6gadaqadaqaamaalaaabaGaeqiUdehabaGaaGOmaaaaaiaawIcacaGLPaaaaaaaaa@60FB@


θ = 2 π f 0 t MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdeNaeyypa0JaaGOmaiabec8aWjaadAgadaWgaaWcbaGaaGimaaqabaGccaWG0baaaa@3D44@ . The closed-form version of the summation requires only three sinusoidal oscillators yet can produce an arbitrary number of sinusoidal components.

Implementing contains one significant challenge, however. Note the ratio of two sinusoids on the far right of the equation. The denominator sinusoid periodically passes through zero, leading to a divide-by-zero error. However, because the numerator sinusoidoperates at a frequency that is N times higher, the numerator sinusoid also approaches zero whenever the lower-frequency denominator sinusoid approaches zero. This "0/0" condition converges to either N or -N; the sign can be inferred by looking at adjacent samples.


  • Moore, F.R., "Elements of Computer Music," Prentice-Hall, 1990, ISBN 0-13-252552-6.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
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Jyoti Reply
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Crow Reply
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RAW Reply
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Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
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The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Stoney Reply
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Adin Reply
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biomolecules are e building blocks of every organics and inorganic materials.
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Source:  OpenStax, Musical signal processing with labview -- subtractive synthesis. OpenStax CNX. Nov 07, 2007 Download for free at http://cnx.org/content/col10484/1.2
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